Summary

Participant selects political party affiliation which then becomes the political party of the majority group.

Majority group opinions deviate away from participant’s choice on 8 issues with possible condition randomly selected (deviation threshold = [0/25/50/75/100%]).

Method change: deviance is tied to specific agents (e.g. the deviant agents are the same from trial to trial)

8 issues, 8 agents

Demographics (Attention Check)
0
(N=68)
0.25
(N=62)
0.5
(N=43)
0.75
(N=63)
1
(N=51)
Overall
(N=287)
age
Mean (SD) 36.2 (13.1) 39.0 (14.9) 36.7 (12.0) 35.1 (11.2) 36.2 (14.2) 36.6 (13.1)
Median [Min, Max] 34.0 [19.0, 67.0] 36.5 [18.0, 74.0] 35.0 [19.0, 68.0] 32.0 [19.0, 65.0] 31.0 [19.0, 72.0] 33.0 [18.0, 74.0]
race
American Indian or Alaska Native 1 (1.5%) 0 (0%) 1 (2.3%) 2 (3.2%) 0 (0%) 4 (1.4%)
Asian 5 (7.4%) 8 (12.9%) 4 (9.3%) 5 (7.9%) 5 (9.8%) 27 (9.4%)
Black or African-American 10 (14.7%) 6 (9.7%) 2 (4.7%) 9 (14.3%) 6 (11.8%) 33 (11.5%)
Hispanic/Latinx 8 (11.8%) 3 (4.8%) 0 (0%) 3 (4.8%) 4 (7.8%) 18 (6.3%)
Other 1 (1.5%) 1 (1.6%) 0 (0%) 0 (0%) 0 (0%) 2 (0.7%)
White 43 (63.2%) 43 (69.4%) 35 (81.4%) 44 (69.8%) 36 (70.6%) 201 (70.0%)
Native Hawaiian or Other Pacific Islander 0 (0%) 1 (1.6%) 1 (2.3%) 0 (0%) 0 (0%) 2 (0.7%)
gender
Man 26 (38.2%) 24 (38.7%) 14 (32.6%) 33 (52.4%) 24 (47.1%) 121 (42.2%)
Woman 42 (61.8%) 34 (54.8%) 27 (62.8%) 26 (41.3%) 26 (51.0%) 155 (54.0%)
Non-binary 0 (0%) 4 (6.5%) 2 (4.7%) 4 (6.3%) 1 (2.0%) 11 (3.8%)
polparty
Democratic 34 (50.0%) 33 (53.2%) 20 (46.5%) 34 (54.0%) 30 (58.8%) 151 (52.6%)
Independent 25 (36.8%) 25 (40.3%) 17 (39.5%) 19 (30.2%) 12 (23.5%) 98 (34.1%)
Republican 9 (13.2%) 4 (6.5%) 6 (14.0%) 10 (15.9%) 9 (17.6%) 38 (13.2%)
0
(N=2)
0.5
(N=3)
0.75
(N=2)
1
(N=4)
Overall
(N=11)
age
Mean (SD) 38.5 (2.12) 32.3 (13.5) 31.0 (9.90) 36.5 (11.6) 34.7 (9.79)
Median [Min, Max] 38.5 [37.0, 40.0] 32.0 [19.0, 46.0] 31.0 [24.0, 38.0] 40.0 [20.0, 46.0] 37.0 [19.0, 46.0]
race
Black or African-American 1 (50.0%) 0 (0%) 0 (0%) 1 (25.0%) 2 (18.2%)
White 1 (50.0%) 3 (100%) 1 (50.0%) 3 (75.0%) 8 (72.7%)
Hispanic/Latinx 0 (0%) 0 (0%) 1 (50.0%) 0 (0%) 1 (9.1%)
gender
Man 1 (50.0%) 1 (33.3%) 2 (100%) 3 (75.0%) 7 (63.6%)
Woman 1 (50.0%) 2 (66.7%) 0 (0%) 1 (25.0%) 4 (36.4%)
polparty
Democratic 1 (50.0%) 1 (33.3%) 1 (50.0%) 2 (50.0%) 5 (45.5%)
Republican 1 (50.0%) 1 (33.3%) 0 (0%) 1 (25.0%) 3 (27.3%)
Independent 0 (0%) 1 (33.3%) 1 (50.0%) 1 (25.0%) 3 (27.3%)
Agent Learning Plots
Learning Analysis
Analysis of Deviance Table (Type II Wald chisquare tests)

Response: corrresp
                                  Chisq Df Pr(>Chisq)    
opinion_round                   249.450  1  < 2.2e-16 ***
Deviant_threshold               173.987  4  < 2.2e-16 ***
opinion_round:Deviant_threshold  32.911  4  1.245e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
 1       opinion_round.trend     SE  df asymp.LCL asymp.UCL z.ratio p.value
 overall               0.253 0.0155 Inf     0.222     0.283  16.340  <.0001

Results are averaged over the levels of: Deviant_threshold 
Confidence level used: 0.95 
$emmeans
 Deviant_threshold emmean    SE  df asymp.LCL asymp.UCL z.ratio p.value
 0                  2.029 0.114 Inf     1.804     2.253  17.721  <.0001
 0.25               0.973 0.114 Inf     0.749     1.197   8.520  <.0001
 0.5                0.648 0.136 Inf     0.381     0.914   4.762  <.0001
 0.75               0.890 0.115 Inf     0.665     1.114   7.766  <.0001
 1                  2.258 0.138 Inf     1.988     2.529  16.378  <.0001

Results are given on the logit (not the response) scale. 
Confidence level used: 0.95 

$contrasts
 contrast                                      estimate    SE  df asymp.LCL
 Deviant_threshold0 - Deviant_threshold0.25      1.0555 0.160 Inf     0.618
 Deviant_threshold0 - Deviant_threshold0.5       1.3811 0.177 Inf     0.899
 Deviant_threshold0 - Deviant_threshold0.75      1.1391 0.161 Inf     0.701
 Deviant_threshold0 - Deviant_threshold1        -0.2294 0.177 Inf    -0.714
 Deviant_threshold0.25 - Deviant_threshold0.5    0.3256 0.177 Inf    -0.156
 Deviant_threshold0.25 - Deviant_threshold0.75   0.0837 0.161 Inf    -0.354
 Deviant_threshold0.25 - Deviant_threshold1     -1.2849 0.178 Inf    -1.770
 Deviant_threshold0.5 - Deviant_threshold0.75   -0.2420 0.177 Inf    -0.724
 Deviant_threshold0.5 - Deviant_threshold1      -1.6105 0.193 Inf    -2.136
 Deviant_threshold0.75 - Deviant_threshold1     -1.3686 0.178 Inf    -1.853
 asymp.UCL z.ratio p.value
     1.493   6.577  <.0001
     1.863   7.816  <.0001
     1.577   7.097  <.0001
     0.255  -1.293  0.6957
     0.807   1.844  0.3483
     0.522   0.521  0.9853
    -0.800  -7.232  <.0001
     0.240  -1.369  0.6476
    -1.085  -8.366  <.0001
    -0.884  -7.709  <.0001

Results are given on the log odds ratio (not the response) scale. 
Confidence level used: 0.95 
Conf-level adjustment: tukey method for comparing a family of 5 estimates 
P value adjustment: tukey method for comparing a family of 5 estimates 
Similarity Analysis
[1] "holding off"
Similarity Analysis
[1] "holding off"
[1] "holding off"
ISM Plot
ISM Analysis
Analysis of Variance Table

Response: k
                   Df Sum Sq Mean Sq F value    Pr(>F)    
Deviant_threshold   4  54.25 13.5617  9.1748 5.558e-07 ***
Residuals         282 416.84  1.4782                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
$emmeans
 Deviant_threshold emmean    SE  df lower.CL upper.CL t.ratio p.value
 0                   1.59 0.147 282     1.30     1.88  10.761  <.0001
 0.25                2.58 0.154 282     2.28     2.89  16.719  <.0001
 0.5                 2.52 0.185 282     2.16     2.89  13.619  <.0001
 0.75                2.69 0.153 282     2.39     2.99  17.578  <.0001
 1                   2.58 0.170 282     2.24     2.91  15.133  <.0001

Confidence level used: 0.95 

$contrasts
 contrast                                      estimate    SE  df lower.CL
 Deviant_threshold0 - Deviant_threshold0.25    -0.99496 0.213 282   -1.581
 Deviant_threshold0 - Deviant_threshold0.5     -0.93848 0.237 282   -1.589
 Deviant_threshold0 - Deviant_threshold0.75    -1.10597 0.213 282   -1.690
 Deviant_threshold0 - Deviant_threshold1       -0.98987 0.225 282   -1.608
 Deviant_threshold0.25 - Deviant_threshold0.5   0.05648 0.241 282   -0.606
 Deviant_threshold0.25 - Deviant_threshold0.75 -0.11101 0.217 282   -0.708
 Deviant_threshold0.25 - Deviant_threshold1     0.00508 0.230 282   -0.626
 Deviant_threshold0.5 - Deviant_threshold0.75  -0.16749 0.240 282   -0.828
 Deviant_threshold0.5 - Deviant_threshold1     -0.05139 0.252 282   -0.742
 Deviant_threshold0.75 - Deviant_threshold1     0.11610 0.229 282   -0.513
 upper.CL t.ratio p.value
   -0.409  -4.660  <.0001
   -0.288  -3.962  0.0009
   -0.522  -5.202  <.0001
   -0.372  -4.395  0.0002
    0.719   0.234  0.9993
    0.486  -0.510  0.9863
    0.636   0.022  1.0000
    0.493  -0.696  0.9571
    0.640  -0.204  0.9996
    0.745   0.507  0.9866

Confidence level used: 0.95 
Conf-level adjustment: tukey method for comparing a family of 5 estimates 
P value adjustment: tukey method for comparing a family of 5 estimates 
 Deviant_threshold emmean    SE  df null t.ratio p.value
 0                   1.59 0.147 282    2  -2.805  0.0027
 0.25                2.58 0.154 282    2   3.766  0.9999
 0.5                 2.52 0.185 282    2   2.832  0.9975
 0.75                2.69 0.153 282    2   4.521  1.0000
 1                   2.58 0.170 282    2   3.386  0.9996

P values are left-tailed 
New Agent Prediction Plot
Prediction Analysis
# A tibble: 2 Ă— 8
  model    term          estimate std.error statistic p.value conf.low conf.high
  <chr>    <chr>            <dbl>     <dbl>     <dbl>   <dbl>    <dbl>     <dbl>
1 below_.5 Deviant_thre…    -38.9      9.80     -3.97 1.06e-4    -58.2     -19.6
2 above_.5 Deviant_thre…     58.3     10.3       5.64 7.67e-8     37.9      78.7
Analysis of Variance Table

Response: confidence
           Df Sum Sq Mean Sq F value    Pr(>F)    
deviance    4  34701  8675.3  14.674 6.674e-11 ***
Residuals 282 166721   591.2                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
$emmeans
 deviance emmean   SE  df lower.CL upper.CL t.ratio p.value
 0          57.2 2.95 282     51.4     63.0  19.386  <.0001
 0.25       40.7 3.09 282     34.7     46.8  13.194  <.0001
 0.5        38.9 3.71 282     31.6     46.2  10.499  <.0001
 0.75       40.4 3.06 282     34.3     46.4  13.177  <.0001
 1          67.2 3.40 282     60.5     73.9  19.736  <.0001

Confidence level used: 0.95 

$contrasts
 contrast                    estimate   SE  df lower.CL upper.CL t.ratio
 deviance0 - deviance0.25      16.420 4.27 282     4.70    28.14   3.846
 deviance0 - deviance0.5       18.232 4.74 282     5.22    31.24   3.848
 deviance0 - deviance0.75      16.797 4.25 282     5.12    28.47   3.950
 deviance0 - deviance1        -10.034 4.50 282   -22.40     2.33  -2.228
 deviance0.25 - deviance0.5     1.812 4.83 282   -11.44    15.06   0.375
 deviance0.25 - deviance0.75    0.377 4.35 282   -11.57    12.32   0.087
 deviance0.25 - deviance1     -26.454 4.60 282   -39.07   -13.83  -5.755
 deviance0.5 - deviance0.75    -1.435 4.81 282   -14.64    11.77  -0.298
 deviance0.5 - deviance1      -28.266 5.03 282   -42.09   -14.44  -5.615
 deviance0.75 - deviance1     -26.831 4.58 282   -39.41   -14.26  -5.858
 p.value
  0.0014
  0.0014
  0.0009
  0.1725
  0.9958
  1.0000
  <.0001
  0.9983
  <.0001
  <.0001

Confidence level used: 0.95 
Conf-level adjustment: tukey method for comparing a family of 5 estimates 
P value adjustment: tukey method for comparing a family of 5 estimates 
Moderator: Last Opinion
0
(N=68)
0.25
(N=62)
0.5
(N=43)
0.75
(N=63)
1
(N=51)
Overall
(N=287)
pred_par
Yes 54 (79.4%) 40 (64.5%) 23 (53.5%) 26 (41.3%) 4 (7.8%) 147 (51.2%)
No 14 (20.6%) 22 (35.5%) 20 (46.5%) 37 (58.7%) 47 (92.2%) 140 (48.8%)
# A tibble: 4 Ă— 9
# Groups:   pred_par [2]
  pred_par id      term  estimate std.error statistic p.value conf.low conf.high
  <lgl>    <chr>   <chr>    <dbl>     <dbl>     <dbl>   <dbl>    <dbl>     <dbl>
1 FALSE    below_… Devi…     6.53      16.9     0.385 7.01e-1    -27.4      40.5
2 FALSE    above_… Devi…    72.3       12.8     5.67  1.36e-7     47.0      97.6
3 TRUE     below_… Devi…   -50.8       11.7    -4.36  2.88e-5    -73.9     -27.7
4 TRUE     above_… Devi…     9.82      21.8     0.450 6.55e-1    -34.0      53.6
Analysis of Variance Table

Response: confidence
                   Df Sum Sq Mean Sq F value    Pr(>F)    
deviance            4  34701  8675.3 15.5658 1.683e-11 ***
pred_par            1   2954  2953.5  5.2994  0.022075 *  
deviance:pred_par   4   9386  2346.4  4.2101  0.002519 ** 
Residuals         277 154381   557.3                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ID with Stimulus Group
Analysis of Variance Table

Response: groupid
                   Df Sum Sq Mean Sq F value    Pr(>F)    
Deviant_threshold   1 117339  117339  269.28 < 2.2e-16 ***
Residuals         285 124187     436                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
 1       Deviant_threshold.trend   SE  df lower.CL upper.CL t.ratio p.value
 overall                   -56.1 3.42 285    -62.8    -49.3 -16.410  <.0001

Confidence level used: 0.95 
ID with PolParty
Type III Analysis of Variance Table with Satterthwaite's method
                       Sum Sq Mean Sq NumDF DenDF F value   Pr(>F)   
Deviant_threshold      125.10   31.27     4   287  0.3531 0.841798   
time                   693.60  693.60     1   287  7.8307 0.005484 **
Deviant_threshold:time 209.02   52.26     4   287  0.5900 0.670163   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Unresolved
  • Similarity Analysis, how to conduct results given the exp design (majority x participant x deviants)

    • Does it make sense to break into deviant/nondeviant learning given design?
  • Learning analysis, how correctness was coded in the learning phase (is button an issue?, show data examples)

  • Last opinion analysis, how to operationalize given the design.

  • U shape analysis, affects all studies